The sides of a triangle are 45, 56, and 36. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse. The triangle is
because the square of the largest side
the sum of the squares of the other two sides.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.